Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier–Stokes equations

Hendrik Ranocha, Lisandro Dalcin, Matteo Parsani

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Recently, relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation. Here, we generalize this approach to guarantee local entropy inequalities for finitely many convex functionals (entropies) and apply the resulting methods to the compressible Euler and Navier–Stokes equations. Based on the unstructured hp-adaptive SSDC framework of entropy conservative or dissipative semidiscretizations using summation-by-parts and simultaneous-approximation-term operators, we develop the first discretizations for compressible computational fluid dynamics that are primary conservative, locally entropy stable in the fully discrete sense under a usual CFL condition, explicit except for the parallelizable solution of a single scalar equation per element, and arbitrarily highorder accurate in space and time. We demonstrate the accuracy and the robustness of the fully-discrete explicit locally entropy-stable solver for a set of test cases of increasing complexity.
Original languageEnglish (US)
Pages (from-to)1343-1359
Number of pages17
JournalComputers & Mathematics with Applications
Volume80
Issue number5
DOIs
StatePublished - Jul 9 2020

Fingerprint Dive into the research topics of 'Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier–Stokes equations'. Together they form a unique fingerprint.

Cite this